Segment Information - Summary of underwriting income or loss by segment (Details) $ in Millions		3 Months Ended		9 Months Ended
		Sep. 30, 2024 USD ($)	Sep. 30, 2023 USD ($)	Sep. 30, 2024 USD ($) segment	Sep. 30, 2023 USD ($)	Dec. 31, 2023 USD ($)
Segment Reporting Information [Line Items]
Number of segments | segment				3
Gross premiums written		$ 5,440	$ 4,527	$ 16,755	$ 14,152
Premiums ceded		(1,393)	(1,172)	(4,842)	(3,945)
Net premiums written		4,047	3,355	11,913	10,207
Change in unearned premiums		(77)	(107)	(956)	(1,111)
Net premiums earned		3,970	3,248	10,957	9,096
Other underwriting income		5	5	20	21
Losses and loss adjustment expenses		(2,403)	(1,647)	(5,958)	(4,609)
Acquisition expenses		(681)	(575)	(1,921)	(1,669)
Other operating expenses		(353)	(310)	(1,062)	(942)
Underwriting income (loss)		538	721	2,036	1,897
Net investment income		399	269	1,090	710
Net realized gains (losses)		169	(248)	358	(354)
Equity in net income (loss) of investment funds accounted for using the equity method		171	59	437	176
Other income (loss)		8	(4)	30	10
Corporate expenses	[1]	(19)	(20)	(88)	(69)
Transaction costs and other	[1]	(30)	0	(55)	(2)
Amortization of intangible assets		(88)	(24)	(136)	(71)
Interest expense		(35)	(34)	(104)	(99)
Net foreign exchange gains (losses)		(63)	22	(31)	(1)
Income (loss) before income taxes and income (loss) from operating affiliates		1,050	741	3,537	2,197
Income tax expense (benefit)		(98)	(72)	(296)	(203)
Income (loss) from operating affiliates		36	54	136	115
Net income available to Arch		988	723	3,377	2,109
Preferred dividends		(10)	(10)	(30)	(30)
Net income (loss) available to Arch common shareholders		$ 978	$ 713	$ 3,347	$ 2,079
Underwriting Ratios
Loss ratio		60.50%	50.70%	54.40%	50.70%
Acquisition expense ratio		17.20%	17.70%	17.50%	18.30%
Other operating expense ratio		8.90%	9.50%	9.70%	10.40%
Combined ratio		86.60%	77.90%	81.60%	79.40%
Goodwill and intangible assets		$ 1,486	$ 739	$ 1,486	$ 739	$ 731
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	2,341	2,043	6,569	5,977
Premiums ceded	[2]	(521)	(521)	(1,649)	(1,564)
Net premiums written		1,820	1,522	4,920	4,413
Change in unearned premiums		(55)	(110)	(226)	(416)
Net premiums earned		1,765	1,412	4,694	3,997
Other underwriting income		0	0	0	0
Losses and loss adjustment expenses		(1,087)	(812)	(2,789)	(2,276)
Acquisition expenses		(308)	(269)	(872)	(778)
Other operating expenses		(250)	(202)	(718)	(592)
Underwriting income (loss)		$ 120	$ 129	$ 315	$ 351
Underwriting Ratios
Loss ratio		61.60%	57.50%	59.40%	57.00%
Acquisition expense ratio		17.40%	19.10%	18.60%	19.50%
Other operating expense ratio		14.10%	14.30%	15.30%	14.80%
Combined ratio		93.10%	90.90%	93.30%	91.30%
Goodwill and intangible assets		$ 1,025	$ 220	$ 1,025	$ 220
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	2,763	2,138	9,171	7,142
Premiums ceded	[2]	(818)	(576)	(3,013)	(2,145)
Net premiums written		1,945	1,562	6,158	4,997
Change in unearned premiums		(53)	(19)	(820)	(781)
Net premiums earned		1,892	1,543	5,338	4,216
Other underwriting income		2	2	5	9
Losses and loss adjustment expenses		(1,317)	(870)	(3,206)	(2,379)
Acquisition expenses		(374)	(304)	(1,050)	(875)
Other operating expenses		(54)	(61)	(193)	(203)
Underwriting income (loss)		$ 149	$ 310	$ 894	$ 768
Underwriting Ratios
Loss ratio		69.60%	56.40%	60.10%	56.40%
Acquisition expense ratio		19.80%	19.70%	19.70%	20.70%
Other operating expense ratio		2.90%	3.90%	3.60%	4.80%
Combined ratio		92.30%	80.00%	83.40%	81.90%
Goodwill and intangible assets		$ 113	$ 132	$ 113	$ 132
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[2]	339	347	1,020	1,037
Premiums ceded	[2]	(57)	(76)	(185)	(240)
Net premiums written		282	271	835	797
Change in unearned premiums		31	22	90	86
Net premiums earned		313	293	925	883
Other underwriting income		3	3	15	12
Losses and loss adjustment expenses		1	35	37	46
Acquisition expenses		1	(2)	1	(16)
Other operating expenses		(49)	(47)	(151)	(147)
Underwriting income (loss)		$ 269	$ 282	$ 827	$ 778
Underwriting Ratios
Loss ratio		(0.40%)	(12.10%)	(4.00%)	(5.30%)
Acquisition expense ratio		(0.40%)	0.60%	(0.10%)	1.80%
Other operating expense ratio		15.60%	16.20%	16.30%	16.70%
Combined ratio		14.80%	4.70%	12.20%	13.20%
Goodwill and intangible assets		$ 348	$ 387	$ 348	$ 387

[1] Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

[2] Certain assumed and ceded amounts related to intersegment transactions are included in individual segment results. Accordingly, the sum of such transactions for each segment does not agree to the total due to eliminations.